T  A 


UC-NRLF 


315    3M7 


G!FT  OF 


•A'K 


I 


>^      v\ 


BUREAU  OF  YARDS  AND  DOCKS, 

NAVY  DEPARTMENT, 
Washington,  D.  C.,  September  15,  1917. 

STANDARDS  OF  DESIGN,  REINFORCED  CON- 
CRETE. 


Details  of  construction. 

1.  Materials,  methods  of  mixing,  placing  and  finishing,  character  of 
forms,  inspection,  etc.,  shall  be  in  strict  accordance  with  the  require- 
ments of  Navy  Standard  Specification,  concrete  and  mortar,  59C2c. 

2.  Protective  covering. — The  minimum  thickness  of  concrete  or 
mortar  for  protection  of  metal  against  corrosion  shall  be  1  inch. 

The  minimum  thickness  of  concrete  or  mortar  for  protection  of 
metal  against  fire  shall  be  a?  follows: 

Inches. 

Columns  and  girders 2 

Floor  beams 1  1/2 

Slabs 1 

The  above  dimensions  are  from  face  of  rod  to  face  of  concrete.  To 
determine  distance  from  face  of  concrete  to  center  of  steel  add  half 
the  diameter  of  the  rods  to  the  above  dimensions. 

All  corners  and  edges  of  columns,  girders,  and  beams  shall  be  either 
beveled  or  rounded. 

3.  Splicing  reinforcing  material  and  joints  in  reinforced  concrete  con- 
struction.— Where  tension  or  compression  reinforcement  is  spliced  it 
shall  be  lapped  on  the  basis  of  the  bond  stress  and  the  stress  in  the 
bar  at  the  point  of  splice,  or  a  connection  shall  be  made  between  the 
bars  of  sufficient  strength  to  carry  the  stress. 

In  columns,  small  rods  (34  inch,  and  under)  shall  be  lapped  as 
ified  above,  and  structural  shapes  or  heavy  bars  shall  be  properly 
spliced  and  provided  with  bearing  plates  at  foundations;  rods 
above  34  inch  shall  be  squared  and  butted  in  sleeves,  and  in  foun- 
dations bearing  plates  shall  be  provided,  or  the  bars  shall  be  carried 
into  the  footing  a  sufficient  distance  to  transmit  the  stress  of  the 
steel  to  the  concrete  by  means  of  the  bond  resistance. 

'<7  points. — Whenever  it  is  found  impossible,  owing  to 
the  magnitude  of  the  work,  to  cast  the  entire  structure  in  one  opera- 
tion, the  following  locations  shall  govern  for  stopping  points  for  the 
respective  parts:  Joints  in  columns  shall  be  flush  with  bottom 
surface  of  girders,  and  in  flat  slab  construction  at  the  bottom  of  the 
flare  of  the  column  head;  joints  in  girders  shall  be  at  center  of  span, 
unless  a  floor  beam  intersects  the  girder  at  this  point,  in  which  case 

16163—17 


3C9526 


the  joint  shall  be  offset  a  distance  equal  to  at  least  twice  the  width 
of  the  beam;  joints  in  floor  beams  and  slabs  shall  be  at  the  center  of 
the  span.  All  joints  shall  be  perpendicular  to  the  axis  or  surface  of 
the  member  jointed.  In  every  case  planes  of  cleavage  caused  by 
stoppage  of  work  shall  be  provided  with  offsets  and  extra  reinforce- 
ment, if  necessary,  to  develop  the  full  designed  strength. 

5.  General  assumptions. — 'Slabs  and  floor  beams  shall  be  designed 
to  support  the  total  dead  and  live  loads;  girders  shall  be  designed  to 
support  the  total  dead  load  and  80  per  cent  of  the  live  load  and 
columns  shall  be  designed  for  the  total  dead  load  and  75  per  cent  of 
the  live  load,  except  as  noted  below.    For  roof  loads  the  full  live 
load  shall  be  used.    In  storehouses  80  per  cent  of  the  live  load 
shall  be  used  on  columns  only;  beams  and  girders  shall  carry  full 
live  load.    Proper  provision  shall  be  made  for  the  dynamic  effect 
of  live  load,  where  same  justifies  consideration,  by  the  addition  of  a 
percentage.    In  special  cases,  where  conditions  justify,  girders  and 
columns  shall  be  designed  for  100  per  cent  of  the  live  load  in  addi- 
tion to  the  total  dead  load. 

6.  Span  lengths  of  slabs,  beams,  and  girders,  and  column  lengths. — 
The  span  length  for  slabs,  beams,  and  gilders,  simply  supported, 
shall  be  taken  as  the  distance  from  center  to  center  of  supports  with 
a  maximum  span  length  of  the  clear  distance  between  supports  plus 
the  depth  of  girder  or  slab.    For  continuous  or  restrained  beams 
the  span  length  shall  be  taken  as  the  clear  distance  between  faces  of 
supports  exclusive  of  brackets.    The  length  of  column  shall  be  taken 
as  the  maximum  unsupported  length. 

7.  Spacing  of  rods. — The  lateral  spacing  of  parallel  bars  shall  not 
be  less  than  3  diameters  from  center  to  center  and  not  less  than  2 
diameters  from  side  of  beam  to  center  of  rod.    The  clear  space 
between  2  layers  of  bars  shall  not  be  less  than  1  inch.    The  use  of 
more  than  2  layers  will  not  be  allowed  unless  special  reasons  make 
same  imperative,  in  which  case  special  provisions  shall  be  made 
for  tying  together. 

8.  Columns. — For  columns  reinforced  longitudinally  and  with  or 
without  spiral  hooping,  the  ratio  of  unsupported  length  of  column 
to  its  least  over-all  diameter  shall  not  exceed  15.    For  columns 
reinforced  with  spiral  hooping  only,  this  ratio  shall  not  exceed  10. 
In  no  case  shall  the  least  over-all  diameter  be  less  than  12  inches. 
The  protective  covering  over  the  steel  shall  be  2  inches.    The 
effective  area  of  hooped  columns  shall  be  taken  as  the  area  within 
the  perimeter  inclosing  the  spiral.    Longitudinal  reinforcement 
shall  not  exceed  4  per  cent  nor  be  less  than  1  per  cent  of  the  effective 
area.    The  total  amount  of  spiral  or  hooping  reinforcement  shall  not 
be  less  than  1  per  cent  of  the  volume  of  the  column,  inclosed.    The 
clear  spacing  between  hoops  shall  not  exceed  1/6  of  the  diameter 
of  the  inclosed  column,  and  shall  in  no  case  be  greater  than  2  1/2 
inches. 

Where  structural  steel  shapes  are  used  for  reinforcing  columns, 
they  shall  be  provided  with  lattice  bars  or  plates  to  tie  them  together, 
no  dependence  being  placed  on  the  concrete  for  this  purpose.  All 
splices,  connections,  etc.,  shall  be  designed  in  strict  accordance 
with  structural  steel  practice. 


9.  Reinforcement  for  shrinkage  and  temperature  stresses. — Reinforce- 
ment should  be  equal  to  about  1/3  of  1  per  cent  and  should  be  of  a 
form  to  develop  high  bond  resistance.    It  shall  be  placed  near  ex- 
posed surface  and  shall  be  well  distributed. 

10.  T-beams. — Where  a  floor  slab  and  beam  are  built  as  a  mono- 
lithic structure,  the  width  of  that  portion  of  the  slab,  which  is  used 
as  the  flange  of  the  T  beam,  shall  not  exceed  the  width  of  the  stem 
plus  eight  times  the  thickness  of  the  slab;  also  it  shall  not  exceed 
three  times  the  width  of  the  stem.    For  isolated  beams  the  width  of 
the  flange  shall  not  exceed  three  times  the  width  of  the  stem.    In 
all  cases  the  total  width  of  flange  shall  not  exceed  one-fourth  of  the 
length  of  the  span. 

11.  Maximum  allowable  unit  stresses  and  ratio  of  moduli  of  elas- 
ticity.— The  allowable  unit  stresses  shall  be  the  percentages  given 
herein  of  the  ultimate  strength  of  the  particular  concrete  which  is 
to  be  used,  as  shown  in  the  following: 

Table  of  ultimate  compressive  strengths  of  different  mixtures  of  concrete. 
[In  pounds  per  square  inch.] 


Aggregate. 

1:1:2 

1:1  J  a 

1:2:4 

1:2J:5 

15:6 

Granite,  trap  rock  gravel,  hard  limestone,  and 
hard  sandstone 

3  000 

2  500 

2  000 

1  600 

1  300 

Soft  limestone  and  sandstone  

2,200 

1,800 

1,500 

1,200 

1,000 

Cinders  .  

800 

700 

600 

500 

400 

ALLOWABLE    UNIT   STRESSES   FOR   PIERS   AND    FOUNDATION'S. 

(a)  Plain  bearing  on  a  concrete  surface  of  at  least  twice  the  loaded 
area,  35  per  cent  of  compressive  strength. 

(6)  Plain  bearing  on  other  surfaces,  25  per  cent  of  compressive 
strength. 

(c)  Axial  compression  in  a  plain  concrete  pier,  the  length  of  which 
does  not  exceed  four  diameters,   22.5  per  cent  of   compressive 
strength. 

ALLOWABLE   UNIT  STRESSES  FOR   SLABS,   BEAMS,   AND  GIRDERS. 

(d)  Compression  in  extreme  fibers  of  concrete,  32.5  per  cent  of 
compressive  strength. 

^  (e)  Compression  in  extreme  fibers  of  concrete  at  supports  of  con- 
tinuous beams,  37.5  per  cent  of  compressive  strength. 

(/)  Vertical  shearing  stress,  horizontal  bars  only  and  without  web 
reinforcement,  2  per  cent  of  compressive  strength. 

(<7)  Vertical  shearing  stress,  bent-up  bars  only  and  without 
vertical  stirrups,  3  per  cent  of  compressive  strength. 

(h)  Vertical  shearing  stress,  combination  of  bent-up  bars  and 
vertical  stirrups  fastened  securely  to  the  bars  and  spaced  horizon- 
tally not  more  than  one-half  of  the  depth  of  the  beam,  5  per  cent  of 
compressive  strength. 


(i)  Punching  shear  with  diagonal  tension  provided  for,  6  per  cent 
of  compressive  strength. 

The  unit  shearing  stress  shall  be  computed  by  formula  22,  given 
in  the  appendix. 

In  providing  for  diagonal  tension  the  web  reinforcement  shall  be 
designed  to  take  two- thirds  of  the  total  vertical  shear. 

ALLOWABLE    UNIT   BOND   STRESS. 

(j)  Bond  between  concrete  and  plain  bars,  4  per  cent  of  compres- 
sive strength. 

(&)  Bond  between  concrete  and  deformed  bars,  5  per  cent  oi 
compressive  strength. 

(I)  Bond  between  concrete  and  drawn  wire,  2  per  cent  of  com- 
pressive strength. 

ALLOWABLE    UNIT   STRESSES    IN    COLUMNS. 

(m)  Columns  with  longitudinal  bars  held  by  bands,  the  bars 
being  not  less  than  1  per  cent  nor  more  than  4  per  cent  of  the  area 
of  the  column  core,  the  bands  being  not  less  than  1/4  inch  in  diameter 
and  approximately  12  inches  on  centers,  shall  have  a  unit  stress  on 
the  concrete  core  not  to  exceed  25  per  cent  of  the  compressive 
strength. 

(ri)  Columns  with  close  hoops  or  spirals  only,  of  not  less  than 
1  per  cent  of  the  column  core  and  spaced  not  more  than  one-sixth 
of  the  diameter  of  the  column  core  nor  more  than  2  1/2  inches  on 
centers,  shall  have  a  unit  stress  on  the  concrete  core  not  to  exceed 
27  per  cent  of  the  compressive  strength. 

(o)  Columns  with  close  hoops  or  spirals  and  with  longitudinal 
bars  all  within  the  limits  specified  above,  shall  have  a  unit  stress 
on  the  concrete  core  not  to  exceed  33  1/3  per  cent  of  the  compres- 
sive strength,  and  in  no  case  to  exceed  800  pounds  per  square  inch. 

ALLOWABLE    UNIT   STRESS   IN    STEEL   REINFORCEMENT. 

(p)  The  tensile  or  compressive  stress  in  steel  shall  not  exceed 
16,000  pounds  per  square  inch.  Steel  in  compression  shall  be 
considered  to  be  stressed  "n"  times  the  stress 'in  the  adjacent  con- 
crete, where  "n"  represents  the  ratio  of  the  modulus  of  elasticity 
of  steel  to  that  of  concrete,  as  given  below. 

MODULI  OF  ELASTICITY. 

In  designing  reinforced  concrete,  the  ratio  of  the  modulus  of 
elasticity  of  steel  to  the  modulus  of  elasticity  of  concrete  shall  be 
taken  as — 

(q)  Forty,  when  the  compressive  strength  of  the  concrete  does 
not  exceed  800  pounds  per  square  inch. 

(r)  Fifteen,  when  the  compressive  strength  of  the  concrete  is 
greater  than  800  pounds  per  square  inch  and  less  than  2,200  pounds 
per  square  inch. 


(s)  Twelve,  when  the  compressive  strength  of  the  concrete  is 
greater  than  2,200  pounds  per  square  inch  and  less  than  2,900 
pounds  per  square  inch. 

(t)  Ten,  when  the  compressive  strength  of  the  concrete  is  greater 
than  2.900  pounds  per  square  inch. 

12.  STANDARD  NOTATION. 

RECTANGULAR    BEAMS. 

The  following  notation  shall  be  used: 
/„= tensile  unit  stress  in  steel. 
/0= compressive  unit  stress  in  concrete. 
Es= modulus  of  elasticity  of  steel. 
£Ie=modulus  of  elasticity  of  concrete. 


3f=moment  of  resistance,  or  bending  moment  in  general,  in 

inch-pounds. 
A= steel  area  in  square  inches. 

6= breadth  of  beam  in  inches. 

d=  depth  of  beam,  to  center  of  steel,  in  inches. 

k= ratio  of  depth  of  neutral  axis  to  effective  depth  d. 

2= depth  of  resultant  compression  below  top. 

.?=ratio  of  lever  arm  of  resisting  couple  to  depth  d. 
jd=d—z=a,rm  of  resisting  couple. 

p= steel  ratio  (not  percentage). 
w/'=load  per  lineal  foot  of  slab  or  beam. 

?=length  of  span  in  feet. 

T-BEAMS. 
6=width  of  flange. 
b'= width  of  stem. 
£=thickness  of  flange. 

BEAMS    REINFORCED   FOR   COMPRESSION. 

-A=area  of  compressive  steel. 
;/= steel  ratio  for  compressive  steel. 
//s= compressive  unit  stress  in  steel. 

C= total  compressive  stress  in  concrete. 
(7=total  compressive  stress  in  steel. 
c?'=depth  to  center  of  compressive  steel. 

2=depth  of  resultant  of  C  and  C". 

SHEAR  AND   BOND. 

V=  total  shear. 
v= shearing  unit  stress. 

u=bond  stress  per  unit  superficial  area  of  bar. 
o= circumference  or  perimeter  of  bar. 
20=sum  of  the  perimeters  of  all  bars. 


COLUMNS. 

A=  total  net  area. 
J.g=area  of  longitudinal  steel. 
-4c=area  of  concrete. 

P=  total  safe  load. 

DESIGN. 

13.  Beams  and  slabs. 
(a)  Continuous  spans: 

Slabs   ^  wl2  at  center  and  over  supports. 
Beams  ^  wl2  at  center  and  over  supports  for  interior  spans. 
fa  wl2  at  center  and  over  support  for  end  span  of  a  series. 
Beams  and  slabs  %  wl2  over  center  support  for  2  spans  only. 

•fa  wl2  at  center  of  spans  for  2  spans  only. 

At  ends  of  continuous  beams  the  amount  of  negative  moment 
depends  on  the  form  of  construction. 

No  smaller  moments  than  the  above  shall  be  allowed  over  supports 
even  if  more  reinforcement  is  put  in  at  the  center  of  the  span. 
Steel  on  compression  side  may  be  considered  as  acting. 
(6)  Ends  free  and  simply  supported: 
Beams  and  slabs  %  wl2  at  center. 

14.  Slabs    supported  along    four    sides  and  reinforced  in    two 
directions. 

(a)  Square  slabs.  —  One-half  the  load  shall  be  considered  as  carried 
by  each  system  of  reinforcement. 


(6)  Rectangular  slabs.—  If  w  is  the  total  load  per  square  foot, 
I  and  Zt  are  the  length  and  breadth  of  panel  respectively  in  feet  and 

r=  ,-,  then  the  load  per  square 

*i 
of  reinforcement  shall  be  taken 


r=  ,-,  then  the  load  per  square  foot  carried  by  the  transverse  system 


wr4 
or 


and  the  load  per  square  foot  carried  by  the  longitudinal  system  shall 
be  taken 


w 


Assuming  these  unit  loads  as  determined  above  for  (a)  and  (6), 
two-thirds  of  the  calculated  moments  shall  be  assumed  as  carried  by 
the  center  half  and  one-third  by  the  outside  quarters  of  each  system 
of  reinforcement. 

15.  Stirrups  should  be  spaced  by  the  formula: 

16000« 


(u-40)6 
for  1:2:4  concrete  where 

v=unit  shearing  stress,  see  formula  (22)  of  the  Appendix. 
6=breadth  of  beam  in  inches. 
s=distance  between  stirrups  in  inches. 
a — cross-sectional  area  of  1  stirrup  in  square  inches. 
Note. — The  unit  shear  on  cross  section  should  never  exceed  120 
pounds  per  square  inch. 


If  main  reinforcing  rods  are  bent  up  for  web  reinforcement,  the 
points  of  bending  shall  be  calculated.  For  this  purpose  the  method 
used  for  designing  cover  plates  of  built-up  steel  girders  is  applicable, 
the  formula  for  uniform  load  on  a  simply  supported  beam  being: 

L'       /a' 

L=-\A 

where  L7=length  of  horizontal  part  of  bent  rods. 

L  =span  length. 

of  =area  of  bent  rods. 

A  —  total  area  of  reinforcement. 

For  continuous  beams,  bending  up  at  the  1/4  points  will  be  satis- 
factory, but  sufficient  steel  must  be  placed  top  and  bottom,  on  each 
side  of  the  quarter  points,  to  take  care  of  the  stresses  resulting  from 
irregular  loads. 

16.  In  girders  and  beams  use  1:2:4  concrete  and  the  following 
maximum  unit  stresses: 

Tension  in  steel pounds. .  16,000 

Compression  in  concrete do 650 

This  gives — 

M=     0.3786d 

jd=     0.8738d 

A=     0*.0077  bd 

17.  Outside  work,  such  as  piers,  wharves,  sea  walls,  etc.,  shall  not 
exceed  the  following  unit  stresses  used  in  their  design: 

Tension  in  steel pounds . .  12, 500 

Compression  in  concrete do 600 

This  gives— 

A=     o!oi  bd 
jd=     o!861d 


APPENDIX. 

The  formulae  given  in  the  above  standards  are  based  on  the  fol- 
lowing general  formulae,  which  were  compiled  by  the  committee  on 
concrete  and  reinforced  concrete,  appointed  by  the  American 
Society  of  Civil  Engineers: 

1.  RECTANGULAR  BEAMS. 


ir 


Position  of  neutral  axis, 

k 
Arm  of  resisting  couple, 


y-i-i* 


(i) 


(2) 


(For/8=15,000  to  16,000,  and/c=600  to  650,  k  may  be  taken  at  *) 
Fiber  stresses, 

M 


,  __ 
J*    Ajd    pjbd* 

2_^_2p/8 
Jo~jkbd*~  k 

Steel  ratio,  for  balanced  reinforcement, 


(3) 
(4) 


P=2- 


/cWc 

(8) 


9 

2.  T-BEAMS. 


A 

i 

jf 

'/* 

d 

X 

/ 

x 

u 

Cose  /.  When  the  neutral  axis  lies  in  the  flange,  use  the  formulas  for 
rectangular  beams. 

Case  II.  When  the  neutral  axis  lies  in  the  stem,  the  following  formulas 
neglect  the  compression  in  the  stem: 

Position  of  neutral  axis, 


kd-- 


2ndA+  bt* 


~2nA  +2bt 
Position  of  resultant  compression, 


_Skd-2t     t_ 
z~2kd-t*   3 


Arm  of  resisting  couple, 
Fiber  stresses, 


jd=d-z 

f      M 

J*~Ajd 


Mkd      _/,       k 
Jo~bt(kd-$t)jd~  n    1-fc 


(6) 

(7) 

(8) 

(9) 

(10) 


(For  approximate  results  the  formulas  for  rectangular  beams  may 
be  used.) 

The  following  formulas  take  into  account  the  compression  in  the 
stem;  they  are  recommended  where  the  flange  is  small  compared 
with  the  stem: 

Position  of  neutral  axis, 


kd-- 


=     2ndA+(b-b')t3 


nA+(b-b')t 


(11) 


10 


Position  of  resultant  compression, 


jd=d—z 


t(2M-t)b+(kd-t)*b' 

Arm  of  resisting  couple, 
Fiber  stresses, 

J^Ajd 
2  MM 


(12) 

(13) 
(14) 

(15) 


3.  BEAMS  REINFORCED  FOR  COMPRESSION. 
fc 


Position  of  neutral  axis, 


Position  of  resultant  compression, 


Arm  of  resisting  couple, 


jd=d—  z 


(16) 


(17) 


(18) 


11 

Fiber  stresses, 


nr  (20) 


4.  SHEAR,  BOKL,  AND  WEB  REINFORCEMENT. 

In  the  following  formulas  2_  refers  only  to  the  bars  constituting 
the  tension  reinforcement  at  the  section  in  question,  and  jd  is  the 
lever  arm  of  the  resisting  couple  at  the  section. 

For  rectangular  beams, 

-133  (22) 

-£  (23) 

(For  approximate  results  j  may  be  taken  as  |.) 
The  stresses  in  web  reinforcement  may  be  estimated  by  the  fol- 
lowing formulas: 
Vertical  web  reinforcement. 

P-g  (24) 


Web  reinforcement  inclined  at  45°  (not  bent-up  bars), 


(25) 


in  which  P=stress  in  single  reinforcing  member,  T7==amount  of  total 
shear  assumed  as  carried  by  the  reinforcement,  and  s=horizontal 
spacing  of  the  reinforcing  members. 

The  same  formulas  apply  to  beams  reinforced  for  compression  as 
regards  shear  and  bond  stress  for  tensile  steel. 

For  T  beams, 

-5?3  (26) 

<27) 


12 

(For  approximate  results  j  may  be  taken  at  f.) 

5.  COLUMNS. 
Total  safe  load, 

Unit  stresses, 

S°=A[l+(n-l)p\ 

/.=»'/„  (30) 


THE  FLAT  SLAB  FLOOR  WITHOUT  BEAMS. 

1.  SYMBOLS  FOR  SQUARE  PANELS. 

I  =distance  center  to  center  of  columns  in  feet  measured 

along  the  side  of  a  square  panel. 
C=  diameter  of  column  capital  in  feet  measured  on  the 

bottom  surface  of  the  slab  or  dropped  panel. 
5=  side  of  square  dropped  panel  in  feet. 
B=  width  of  any  band  of  rods  in  feet. 
u'=sum  of  live  and  dead  loads  in  pounds  per  square  foot. 
M=  bending  moment  in  foot-pounds. 
d=  effective  depth  of  slab  in  inches. 
D—  effective  depth  of  dropped  panel  in  inches. 
t=  total  thickness  of  slab  in  inches. 
T=  total  thickness  of  dropped  panel  in  inches.    Other  sym- 

bols are  those  used  in  the  Standard  Notation. 

2.  FOUR-WAY  SYSTEM  WITH  DROPPED  PANEL. 

The  following  formulas  shall  be  used  in  design: 
£=0.42Z. 
C=0.225Z. 


d=,  on  basis  of  moment,  for  w  not  greater  than  440 
61 

pounds  and  p=0.77  per  cent. 

d=^-~=Q,  on  basis  of  shear,  for  w  greater  than  440  pounds. 

L.£to 

D=1.5rf. 
t=d-\-  1.5  inches. 
T=Z>+2  inches. 

Total  negative  M  at  column  (in  any  direction)=0.032w;Z3. 

Positive  3/at  middle  of  bands=0.012wZ3. 

Negative  M  over  middle  of  side  bands=0.009wP. 

NOTE.  —  The  above  proportions  for  S,  C,  B,  and  D  make  it  neces- 
sary to  solve  only  two  of  the  other  formulas.  Assume  a  total  thick- 
ness, t,  to  determine  a  tentative  value  of  w.  Solve  for  d  and  deter- 
mine the  correct  value  of  w  .  D  then  becomes  1.5rf.  Find  the  posi- 
tive moment  at  the  middle  of  the  bands  from  the  formula  positive 
jtf=0.012w;Z3.  From  the  moment  thus  found  find  the  amount  of 
positive  steel  required  at  .the  middle  of  each  band.  Carry  this  same 
amount  of  steel  over  the  column  in  each  band,  which  will  take  care 
of  the  total  negative  moment  at  the  column.  Finally,  take  three- 
fourths  of  this  positive  steel  and  distribute  it  in  the  top  of  the  slab 
over  the  side  bands  and  over  the  central  half  of  the  panel  to  take 
care  of  the  negative  moment  at  the  middle  of  the  side  bands. 

(13) 


14 

3.  Two-WAr  SYSTEM  WITH  DROPPED  PANEL. 

The  following  formulas  shall  be  used  in  design: 
S=OAl 
C=0.225Z. 
£=0.4Z. 

^=-E7p  on  basis  of  moment,  for  w  not  greater  than  576 

pounds  and  p=0.77  per  cent. 
^=f2Q0»  on  basis  of  shear,  for  w  greater  than  576  pounds. 

D=1.25c?,  for  p=1  per  cent. 
£=e/-f-l. 5  inches. 

T=D+2  inches. 

Negative  Mat  column  for  each  band=0.034:?/;Z3. 
Positive  M  at  middle  of  side  band=0.0174:wZ3. 
Negative  M  over  middle  of  side  band=0.015wZ3. 
Positive  M  at  middle  of  center  band=0.008wZ3. 

4.  DETAILS  OF  CONSTRUCTION. 

The  above  formulas  apply  to  square  panels  and  uniformly  dis- 
tributed live  loads.  For  heavy  concentrated  loads  special  provision 
will  have  to  be  made  by  the  use  of  beams  or  girders. 

The  diameter  of  the  column  capital  shall  be  considered  to  be 
measured  where  its  vertical  thickness  is  at  least  1  1/2  inches,  pro- 
vided the  slope  of  the  capital  below  this  point  nowhere  makes  an 
angle  with  the  vertical  of  more  than  45  degrees. 

Points  of  inflection  on  any  line  joining  two  column  centers  may 
be  taken  as  one-fifth  of  the  clear  distance  on  that  line  between  the 
perimeters  of  the  column  capitals  and  measured  from  the  perime- 
ters. 

If  the  length  of  end  panels  is  made  equal  to  0.9  of  the  length  of 
interior  panels,  it  will  not  be  necessary  to  compute  the  moments 
for  end  panels,  and  the  same  distribution  of  steel  may  be  used  in 
both  end  and  interior  panels. 

Punching  shear  at  the  face  of  the  column  shall  not  exceed  120 
pounds  per  square  inch. 

5.  RECTANGULAR  PANELS  WITH  UNEQUAL  SIDES. 

The  following  applies  to  both  the  four-way  and  the  two-way 
systems: 

In  determining  the  thickness  of  slabs  and  dropped  panels  the 
factor  Z,  occurring  in  the  formulas  for  thickness,  shall  be  the  longest 
side  distance  center  to  center  of  columns. 

In  determining  moments  in  side  bands  and  center  bands  the 
factor  Z,  occurring  in  the  formulas  for  moments,  shall  be  the  distance 
center  to  center  of  columns  parallel  to  the  band  in  question. 

In  determining  moments  in  diagonal  bands  the  factor  I,  occurring 
in  the  formulas  for  moments,  shall  be  the  average  of  the  two  side 
distances  center  to  center  of  columns. 


THIS  B*OOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN     INITIAL     FINE     OF    25     CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


NOV  11  1932 

JUN  3  0  20fl1 


LD  21-50m-8,'32 


36952G 


YB  51932 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


